We are concerned with the numerical simulation of certain multi-fluids flows, which in particular arises in the modeling of pollutant spreading and powder--snow avalanches. The behavior of the mixture is described through a single mass density and a velocity field, with an unusual constraint that relates the divergence of the velocity to derivatives of the density. We propose a numerical scheme based on a hybrid Finite Volume/Finite Element method. This approach is validated by comparison to analytical solutions and experimental data. The scheme works on unstructured meshes and it can be advantageously coupled to mesh refinements strategies in order to follow fronts of high density variation. We pay a specific attention to the behavior with respect to the leading coefficients that characterize the flow: the Froude and Reynolds numbers.